Band-pass filter



D 1936. H. A. WHEELER BAND PA's s FILTER Filed June 10, 1935 3Sheets-Sheet 1 RECEIVER BAND P/IJS FILTER i- -o I 1 {7-49 64w PASS mm?INVENTOR. 054mm A WlfELfR BY RIM/HM ATTORNEY.

Dc. 15, 1936. H, A. WHEELER I 2,064,775

' BAND PASS FILTER Filed June 10, 1935 3 Sheets-Sheet 2 4m zz 4 4b if 5%R if i, MU '& "i

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$3 (J7 INVENTOR- i {2" #49040 A. WHEELER BY W Dec. 15, 1936. H. A.WHEELER BAND PASS FILTER Filed June 10, 1935 3 Sheets-Shee't 3 INVENTOR.flma'om A WHEEL 2 ATTORNEY.

* arrangements of the prior art, and which will re- Patented net. is,case new , attests asa -ease rnrr'sn Application June 10, test, Serialhe. 2553s it iliaims.

My invention relates to band-pass filters and more particularly tocomposite filters including a plurality of separate band-pass filtersco-oper ating to pass a more extended hand than any oi the filtersindividually.

While my invention is or general application, it is especially suitablefor coupling an antenna, adapted toreceive or transmit a wide band or aplurality of bands of the radio-frequency spec= trum, to asignal-translating circuit.

In many installations, particularly in radiofrequency receiving andtransmitting circuits, it is desired to pass a wide band of frequencies,or selectively to pass any of a plurality oi frequency bands aggregatinga wide portion of the radiofrequency spectrum. However, certaindimmities are presented in the design of a band-pass filter operatingbetween extreme frequency limits, both as to the complexity or number offilter elements required and the actual circuit design and as to theprocurement of reasonably uniform responsiveness over the band.

It is an object of my invention, therefore; to provide a compositeband-pass filter capable of passing a wide band of frequencies, whichwill overcome the above-mentioned dimculties oi the quire a minimumotcircuit elements.

More specifically it is an object of my invention to provide a compositeband-pass filter capable oi covering a wide band of frequencies andincluding a plurality of co-operating band-- they may be directlyinterconnected, as by a series connection, without substantiallyaffecting the operation of either filter over its respective band. Theterminal sections, of the other end of the filters are of a type and soproportioned that they may be connected in difierent manners to an inputcircuit, and these latter sections include impedance elements efiectivesubstantially to isolate each input section from the other over itsrespective band. I

For a better understanding of my invention, together with other andfurther objects thereof, reference is had to the following descriptionticularly applicable and in which the invention megacycles.

or riee (or, ire-ssh taken in connection with the accompanying drawings,and its scope -vrill be pointed out in the appended claims.

In the drawings, Fig. 1 is a schematic 511cm of a complete antennasystem including a com- 5 posite band-pass filter employing myinvention; Figs. 2 and 3 are approximately equivalent sim plifiedcircuit diagrams of the system oiFia. i when operating in the short waveand long wave bands, respectively; Figs ioid are circuit 10 diagramsillustrating the circuit transiormations in developing thehigh-frequency filter component; Fiasco-Edam corresponding diagrams forthe low-frequency component of the filter of Fig. 1; Fig. s is acomposite equivalent circuit diagram oi the networks of Figs. i and 5;Figs. "Ia-7d are graphs representing certain operating characteristicsof the primary side of the composite band-pass filter of Fig. 1; whileFigs. tic-8c are graphs of certain operating characteristics of thesecondary side of the filter oi Fig. 1.

Referring now more particularly to Fla. 1, there is shown schematicallya wave-signal collecting system, to which my invention is pariii isembodied as a composite filter for coupling an 25 antenna, for operationover an extended frequency hand or a pluralityaof individual frequencybands, to a sianal-translatmg or load device,such as a radio receiver,either directly, or indirectly by means of a transmission line. Thegeneralsystem of Fig. 1 is disclosed and claimed in my co-pendingapplication Serial No. 25,735, filed June 10, 1935, so that a detailedde scription thereof is considered unnecessary,

In general, the system includes an antenna lea-4th, preferably designedas a doublet for operation in the hiehirequency portion of the band tobe covered but including connections for converting it into a fiat-topantenna tor oporation over the low-frequency band. The antenna ltd-4this coupled to a transmission line it by a high-band filter tie to!balanced operation of both the doublet antenna and the line over ahigh-frequency hand which may, tor errample, extend from 6 to 18megwyfiles. Similarly, the low-hand filter iib couples the antenna, forunbalanced operation asa fiat-top antenna, with the balanced line, foroperation over a low-frequency band, for eizample, of 9.55 to 6 so Thetwo filters areuncoupled on the antenna side because of the balanced andunbalanced operation oi the antenna over the high and low-frequencybands, respectively. They are joined together-on theline side and astheir operation is interdependent at frequencies in the neighborhood ofthe dividing frequency, for example, 6 megacycles. The two filters Ha, Ilb are designed independently and then combined, as will be explainedmore fully hereinafter.

The other end of the line I2 is coupled by a band-pass filter l3, whichmay be of any of several types well-known in the art, to asignaltranslating or load device H having an input circuit the impedanceof which is represented at l5. One type of composite extended-band-passfilter particularly suitable for this purpose is disclosed and .claimedin my copending application, Serial No. 25,737, filed June 10, 1935. I

It is desired that the composite filter shall match the impedance of thedoublet antenna to the constant image impedance of the line over thehigh-frequency range of operation, and that it shall connect the antennaas a fiat-top antenna and match its impedance to that of the line overthe low-frequency portion of the operating band. It is also desirablethat the composite filter cir- I cuit shall include a transformersection which avoids direct connections between the primary andsecondary circuits of the filter and permits impedance transformation.The impedance of the antenna lilal0b, operating as a doublet, is shownin Fig. 7a, in which a value of impedance somewhat greater than thegeometric mean of the antenna impedance over the high-frequency band isindicated by the value Rn.

For the purpose of explanation, the characteristic of Fig. 7a is dividedinto portions separated by the frequencies f1, f2, fa, f4, whicharbitrarily divide the entire frequency band to be covered into threecomponent bands. For example, f1, h, is and f4 may have approximatelythe values 0.55, 1.8, 6 and 18 megacycles, respectively. With respect tothe antenna filter circuits Ila, llb,

the lower frequency band is from fi-h, while.

the upper frequency band is from fa-f4.

The antenna impedance, as shown in Fig. 7a, over the band fs-f4 isapproximated by' the image impedance of a constant-k half-section withmid-series termination facing the doublet antenna. (Fora more completedescription of the several types of band-pass filter sections utilizedin the preferred embodiment-of this invention and discussed herein,reference is made to a textbook of T. E. SheaTransmission Networks andWave Filters, D. Van Nostrand 00., 1929.)

It has become common practice in the design of band-pass filters to makecertain of the computations on the basis of a constant-k filterhalfsection of a standard type, which is adopted as a conventionalreference standard and in terms of which the formulas for some oftheother types are derived and expressed, even though, in certaininstances, sections of this standard type are impedance at each junction-of the sections or' half-sections. For the type generally used as astandard, the input and output image impedances have the same value atthe frequency for which. the slope of their characteristic curves. iszero. This value is indicated by the symbol R, which may be taken as 100ohms, for example, for the purposes of computation. Such a filtersection will be referred to hereinafter as type A. (This type isreferred to' at page. 315 of the Shea reference as type IVK.)

In Fig. 4a is illustrated a constant-k filter halfsection of type A,just described, indicated at A. This filter half-section comprises amid-series condenser l6 and inductance l1 and mid-shunt condenser l8 andinductance I9. Such a halfsection permits the insertion of a transformersince it includes both series and parallel inductances, which may berealized by a transformer in an equivalent network. In computing thecircuit constants of the section A, it wil be assumed that it is to bedesigned for equal values of R of 100 ohmsat both input and outputterminals. The values of the circuit reactances may then be computed, interms of R and the boundary frequencies of the band which the filter isto pass, from the formulas given by Shea for the IVx type on page 316.These formulas are for the so-called full-series and full-shunt" armsand must be modified in the well-known manner for computation of themid-series" or mid-shunt arms employed at the'input and output terminalsof a filter. Alternatively, the circuit constants may be computed bysuch formulas as modified for a half-section (the mid-series terminationreactance one-half the full-series reactance; the

mid-shunttermination reactance twice the fullshunt reactance), and forthe particular boundary frequencies, as given in the appended table offormulas 'for the type A filter section of Fig. 4a. In order to connectadjacent band filters together at one end to form a composite filter, itis desirable to. include at that end of each com-' ponent filter ahalf-section terminated in a mid- I series reactance arm for which maybe substituted reactance elements of the other adjacent band filter.There is represented at B, Fig. 4a, a type of half-section filter bywhich these characteristics can be procured. The filter halfsection Bincludes the parallel-connected midseries condenser 20 and inductance 2iand midshunt condenser 22 and inductance 23. In this type of filter, forthe purposes herein described, the values of the mid-series elements 20,2! are not critical and these elements can be replaced by reactanceelements forming a part of, and critically proportioned for, a bandfilter designed for an adjacent band, without substantially affectingthe operation of this type of filter. The filter halfsection B has atits left-hand terminals .a constant-k mid-shunt image impedance similarin form to that at the right-hand end of the filter section A, so thatif .these two image impedances are made equal, the two sections may bedirectly interconnected. The circuit constants of the filter section Bmay be computed by assuming for R the same valueas for the section A,for example, 100 ohms, and by using the formulas given by Shea forfilter sections of thesame type or by such formulas modified for ahalf-section and for the particular boundary frequencies of this case,as given in the appended table for type B of Fig. 4a.

It will be noted that the formulas for the circuit co nstants of thetype B filter section are in terms of, the parameters m1 and ma.Theoretically, the larger of the parameters mi'and m2 is a function ofthe cut-ofi' frequencies of the filter and the frequency of infiniteattenuation. For the purposes of this application, however, the largerof the values m1 and m: is chosen rather to secure the desired shape of'the mid-series image impedance characteristic and to determine theapproximation of the major portion of this characteristic to a levelvalue. These parameters have no effect on the cut-off frequencieshectare of the filter. In the designing of a type B filter for thehigher of two adjacent bands (of the type 1V4 in Shea), the parameter mais the greater, while in the case of a type B filter for the lower'oftwo adjacent bands (type IV: inShea) m1 is the greater. In either.case the value .of the a value of m onthe order of (Lite 0.5 has beenfound to he the optimum.

Byithe use of well-known equivalent circuit transformations, thehalf-sections A and B of Fig. in can be combined into the high-bandfilter lie of Fig. i. For example, the adjacent termi nals of thesections A and B may he interconnected, and the condensers i8 and 22combined intoa single condenser and the inductances it) and it, into asingle inductance 2Q, since these elements are all connected inparallel. This transformation is shown in Fig. 4b. Similarly, it iswell-known that the inverted-L connection of inductances ii and 2d ofFig. 4b is the equivalent of a transformer in which the inductances iiand 2% provide the self-inductance of the primary circuit, and theinductance 2% provides the mutual inductance andthe self-inductance ofthe secondary circuit, in this case the two latter inductances being ofequal value. The result of this transformation is the circuit of Fig.4c, in which the inductances 2'! and ti are proportioned as justdescribed.

In the computation of the values of the circuit reactances of thecircuit of Fig. 40, however, it is necessary to multiply all of thereactances of the primary circuit by the ratio of the-nominal arrtennaimpedance R1) to the assumed image impedance R. The maximum imageimpedance of the filter at the antenna end will then have the value Rn,as indicated in Fig. 7b, which, as stated above, is somewhat greaterthan the mean value of the antenna'impedar ice over the band, so thatthe image impedance of the line reasonably ap proximates the antennaimpedance over the hand. Similarly, in order to match the secondarycircuit to the line 82; it is necessary to multiply the circuitreactances\ of the secondary circuit by the ratio of the image impedanceof the line 02, R1,, to the assumed image impedance R. The formulas forthe circuit constants of the circuit of Fig. 4c. referred to hereinafteras a type C filter section, including the circuit transformations andthe factorsfor the matching of the primary and secondary impedances, aregiven in the formula for type C of Fig. 4c, in the appended table. The

similarly, by dividing the condenser 30 and informulas for type pfiltersmay be derived from the formulas for types A and B by well-knownalgebraic transformations.

The circuit oflFig. 40 may be rearranged as shown in Fig. 4d, forbalanced operation, by 4 giving to the induct ances 21a and 21b acombined value equal to that of the inductance 2i and,

ductance 3! into two portions represented by the elements 80a, Ma and30b, 3"); In general, the inductancesl'la, 211; will not each have a,value half that of the inductance 21, nor the inductances flu, Slb, halfthatof the inductance 3!,

because of the mutual inductance between con-e sponding portions.Similarly, the component band-pass filter ilb, for operation over thelow-frequency band, for

example, 0.55-6 megacycles, may be designed to couple the antennalilo-4GB, operating as a simple, unbalanced, flat-top antenna, to thebalanced transmission line it and to match the impedances of the antennaand line over the low-frequency band. The antenna characteristicimpedance over this band is shown in Fig. 7c.

The design of the component low-band filter lib is approached from thesame standpoint as that of the high-band filter described above.Referring to Fig. 5a, the starting point is again a standard filterhalf-section of type A having a constant-k image impedance of nominalvalue R,

for example, 1% ohms. The half-section A of Fig.

512 comprises a mid-series condenser 32 and inductance t3, and amid-shunt condenser 34 and 1 inductance 35. The formulas for the circuitconstants of the half-section A of Fig. 5a are given in the appendedtable, Fig. 5a, type A.- It is seen that these formulas are identicalwith those for are similarly applicable to the selection of theright-hand type B half-section of the low-band L- fllter 6 lb. As shownin Fig. 5a, the type B section is similar to the type B section of Fig.4a, and comprises the parallel-connected mid-series condenser 38 andinductance 31, and the mid-shunt condenser 38 and inductance 39. Theonly difference between the type B halfsection of. Fig. 5a and that ofFig. 4a is that in the type B the parameter m1 is greater than me. whilein the latter ma is greater than m1 (parameter m1 is greater or lessthan ma, depending on whether the natural frequency of the mid-shuntelements is greater or less than that of the midseries elements). Theformulas for the type B half-section of Fig. 5a are given in theappended table under'this heading.

While the sections A and B of Fig. 5a could be merged directly into anequivalent network in-' 'cluding a transformer section, as was done inthe case of the high-band filter, for the particular disclosed herein,this transformer would require a coefficient of coupling very close tounity in order to cover the entire 'low-frequency-band f1- is. Thisrequirement may be made less severe by the addition of a transformerfilter section such as the section E of Fig. 5a. The half-sections A 1denser 63, and inductance M. The formulas for computing the. circuitconstants of the type E section of Fig. 5a are given in the appendedtable.

The components A, Band E of Fig. 50. can be mergedinto their electricalequivalents, as indi-' cated in Figs. 5b, 5c and 5d. In Fig. 5b themidthe single condenser 45, the mid-shunt inductances 35 and II into theinductance 46, the midshunt condensers 38 and 43 into the condenser 41,and the mid-shunt inductances 39 and 44 into the inductance 48.- It isseen that the inductances 46, J2 and comprise a pi-section which may bereplaced by an equivalent transformer. 'Such shunt condensers :34 and 40are. combined into operating frequencies and circuit characteristics atransformation is'shown inFig. 5c, inv which these inductancesareconverted into a transformformer 50-52 is effective to match theimpedances of the antenna and the line over the lowfrequency band ;f1fa.,The circuit of F18. 5c is also modified in that the values of thereactance elements of its primary circuit are multiplied by such afactor that the condenser 53 has a capacitance equal to that of theflat-top antenna, efiective at the lowest frequency 11. The nom-' inalvalue of the, antenna impedance and the image impedance of the antennaend of the filter of Fig-5c is then determined by multiplying theassumed nominal image impedance R by the ratio of the capacitance of thecondenser 53 to that of condenser 32. The image impedance characteristicof the antenna end of the filter of Fig. 5c is shown. in Fig. 7d, inwhich the nominal value RE is seen to be slightly greater than the meanantenna. impedance over the band .fij3, as shown in Fig. 7c.

The circuit of Fig. 5c is modified to that of Fig. 5d in order that thesecondary circuit may operate into a balanced line. To this end themidseries condenser 55 and inductance 56 are each divided into equalparts represented by the condensers 55a and 55b and the inductances 56aand 56b of Fig. 5d. In Fig. 5d isshown also a modiflcation of theprimary circuit of Fig. 5c, in which the capacitance 58, representingthe value of antenna capacitance effective, at the lowest frequency ii,is substituted for the mid-series condenser 53, and in which theinductance 59,'representing the inductance requiredto tune withcapacitance 58 to the fundamental frequency is of the antenna, issubstituted for a portion of the mid-series inductance 54 of Fig. 5c.The inductance 51, thus, represents the difference between theinductance 54 and the inductance 59.

The formulas for computing the equivalent filter circuit of Fig. 50,which is referred to hereinafter as type D, are given in the appendedta.- ble. These formulas are derived from the formulas for sections A, Band E of Fig. 50,, taking into consideration the circuit transformationsand multiplying the primary circuit reactances' by the ratio of thenominal antenna impedance Ra to 'the assumed nominal image impedance Rand by multiplying the secondary circuit reactances by the ratio of theimage impedance of the line R1. to the assumed nominal image impedance Rof the section B of Fig. 5a.

It is seen that the arrangement of Fig. 5d is the equivalent of a filtersection with constant-k mid-series termination'on short circuit. Asindicated in Fig. 7d, the image impedance of this arrangement is zero atthe cut-off frequencies, so that the cut-off frequencies of the'circuitare. not affected by the short-circuit and the filter properties of thecircuit are not destroyed.

In Fig. 6 is shown the combination of the highband filter of Fig. 4d andthe low-band filter of Fig. 5d. The primary circuits 'are unchanged, butthe secondary circuits are combined in a particular manner.- Themid-series elements 28 and 29 of Fig. 4d are replaced by elements 5i and52, respectively, of the low-band filter, as shown in Fig. 6, while themid-series elements 55a, 56a, v

55b, 56b of the low-band filter are replaced by the elements 30a, 3|a,30b, 36b, respectively, of the high-band filter. In other words, eachfilter circuit proper operates as a mid-series reactance arm for theother filter. While the circuit constants of each of the filters may notbe ideal for terminating the other; the values of these terminatingreactances are not critical, so that these siderably more abrupt thanthat of'a constant-k section and is characteristic of the mid-seriestermination of the type B filter. Similarly, the image impedancecharacteristic of the type B section of Fig. 5a is shown in Fig. 81). Itis seen that these two filter characteristics are substantiallycomplementary for the entire band fif4. The effect of connectingtogether the highand low-band filters at the terminals of the line l2,as'shown in Fig. 6, is to merge the image impedance curves of the twofilters into a single curve substantially continuous over the bandf1--j4, as shown in Fig. 8c. The characteristic of Fig. 8c is similar tothat of a continuous band filter with constant-k mid-shunt termination,but the composite filter just described secures this characteristic bythe merging of two separate adjacent band filters at one end. Y

The type B filter is fundamentally characterized by having only onefrequency of infinite attenuation in an adjacent band and none outsideof the composite band. I This frequency of infinite attenuation is thenatural frequency of the mid-series reactance arm comprising theparallel resonant circuit. For the purposes described herein, the valuesof the mid-series reactance elements are not critical, so that anadjacent band filter may be substituted therefor, as de-,

scribed above. This characteristic of a frequency of infiniteattenuation in only one adjacent band is fundamentally associated withthe above-described properties of the mid-series image impedance 'ofthis type of filter, as shown in Figs. 8a and 812. These propertiesenable two bandpass filters designed for adjacent frequency bands to becombined into a composite filter having a resultant image impedancecharacteristic as shown in Fig. 80.

It will be seen that the derived circuit of Fig. 6 is equivalent to thatcomprising the high-band and low-band filters liar-l lb of Fig. 1, theinput terminals of the high-band filter being connected to the terminalsof the doublet antenna, which are interconnected through an inductanceM. The input terminals of the low-hand filter are connected,respectively, to the mid-point of the inductance 64 and to the junctionof coils 52a and 52b, into which the coil 52 of Fig. 6 is divided toprovide a ground connection through the line for the antenna Ina-lobwhen operating as a simple fiat-top antenna in the low-frequency band.As an alternative this latter connection may be independently grounded,preferably in the immediate neighborhood of the antenna, as directlyunderneath. The transformer comprising the windings 50 52a and 52b ofthe low-band filter 7 preferably is provided with a core of finelydivided iron.

It is believed that the general principles of operation of theabove-described system will be clear from the foregoing detaileddescription of the circuit arrangements and the principles involved inits design. However, the operation in the inductances of the low-bandfilter lib have such a high impedance that their admittance may beneglected, while the condensers of this filter have such a low reactancethat they may be considered as short circuits.- Similarly, at the lowerfrequencies of the low band, the reactance elements of the high-bandfilter may be neglected. Thus,.the primary circuits of the two'filtersefiectively have separate input circuits of difierent impedances, eventhough they are. connected in a conjugate manner to the same antennastructure.

Referring specifically to Fig. 2, the antenna Eda-lilo operates as abalanced doublet and the high-band filter lie is efiective to couple thebalanced antenna currents to the balanced line it as balancedcirculating currents therein, at the same time approximately matchingthe impedance of the doublet antenna with that of the line over thelot-frequency fs-fc. The circulating currents in the line it are coupledby the filter l3 toinduce unbalanced currents in the input circult to ofthe receiver M.

en operating in the low-frequency band, as illustrated in Fig. 3, thelow-band filter No serves to couple the unbalanced currents of theantenna lilo-lob, operating as a simple flat-top antenna, as balancedcirculating currents in the linel2. The filter 83 similarly couples thebalanced circulating currents of the line l2 into the unbalanced inputcircuit to of the device to. In this hand the line 62 may serve also asa ground leadfor the simple antenna, the connection being made at thejunction between coils 52a and. 52b so that the unbalanced groundcurrents flow in parallel through the conductors l2.

While the filter sections of my invention have been described withreference to primary or input circuits and secondary or output circuits,it will be clear that these designations are by way of illustrationonly, and that power may be transferred through the filters in eitherdirection, so that either end may be considered as the input or output"circuit.

e the composite band filter above-described may be designed foroperation over a wide range of conditions. there are given herewith, byway of example only, the circuit constants of a particular compositefilter embodying myinvention in the form described iii-.1. e iollo 1-1;;circuit values were re rive-L as closely as possible and include suchefiects as erent capacitance or inductance of other related circuitelements:

' System f1= h=1a mecycles i =6 rnycles f6=18 megacyclee dome filterIto-1500 ohms v Rr=1080 ohms I Element =45 mlcrohenries fila+fill1=9microhenries 8lc+tib=5 microhenries tl= microhenries 52a+52b=l2emicrohenries 59=3 microhenries 25:44.2 micro-microiarads 363a, tob=63micro-microiarads each l=59 micrmmicroiarads 5 i =98 micro-microtaradsta=2ao micro-microiurads Transformer 22770., 2%, cm, 86o Coemcient ofcouplina=ii7.8%

Transformer to, 2%, 2th Coefiicient of coupling=89.3%

characterized by a constant-k image impedance at its non-terminal endand by one frequency of infinite attenuation in only each adjacent oneof said bands, each of said half-sections normally including a reactancearm at its terminal end resonant at each of its respective frequenciesof infinite attenuation, each said reactance arm.

being replaced by reactance elements of the filter passing the bandincluding its resonant frequency, and said filters being relativelyproportioned to present across said terminal circuit a resultant imageimpedance approximating that of a constant-7c continuous-band filterpassing the band comprising said contiguous bands.

2. A composite band-pass filter comprising a plurality of individualband-pass filters passing respectively a series of contiguous frequencybands and connected at one end to a common terminal circuit, each ofsaid filters being terminated at said end in a half-section of a typecharacterized by a constant-7c image impedance at its non-terminal endand by one frequency of infinite attenuation in only each adjacent oneof said bands, each of said half-section's normally including areactance arm *at its terminal end resonant at each of its respectivefrequencies of infinite attenuation, each said reactance arm beingreplaced by reactance elements of the filter passing the band includingits resonant frequency, each of the terminal half-sections of thefilters passing the two extreme frequency bands being of type B andproportioned substantially in accordance with the type B formulas, thetwo corresponding frequencies of infinite attenuation being eachpredetermined to give a value within the range 0.25-0.75 for the greaterof mi and m: in the said formulas, and said filters being relativelyproportioned to present across said terminaleircuit a resultant imageimpedance approximating that of a constant-k continuous-band filterpassing the band comprising said contiguous bands.

3. A composite band-pass filter comprising a plurality of individualband-pass filters passing respectively a series of contiguous frequencybands and connected at one end to a common terminal circuit, each ofsaid filters being terminated at said end in a half-section of a typecharacterized by a constant-7c image impedance at its non-terminal endand by one frequency of infinite attenuation in only each adjacent oneof said bands, each of said half-sections normally including a reactancearm at its terminal end resonant at, each of its respective saidfrequencies of infinite attenuation, each said reactance arm beingreplaced by reactance elements of the filter passing the band includingits resonant frequency, each of the terminal half-sections of thefilters passing the two extreme frequency bands being of type B andproportioned substantially in accordance with the type B formulas, thetwo corresponding frequencies of infinite attenuation being eachpredetermined to give a value on the order of 0.4 to 0.5 for the greaterof mi and m: in the said formulas, and said filters being relativelyproportioned to present across said terminal circuit a resultant imageimpedance aproximating that of a constant-k continuous-band filterpassing the band comprising said contiguous bands.

4. A composite band-pass filter comprising a plurality of input circuitsof different impedances and a common output circuit, a plurality ofindividual band-pass filters passing respectively a series 'ofcontiguousfrequency bands and connected to said common output circuit, each ofsaid filters being terminated at said common end in a half-section of atype characterized by one frequency of infinite attenuationin only eachadjacent one of said bands and normally including a reactance arm at itsterminal end resonant at each of its respective frequencies of infiniteattenuation, each said reactance arm being replaced by reactanceelements ofthe filter passing the adjacent band including its resonantfrequency, each of said filters including also one or more impedancematching filter half-sections interconnecting its respective inputcircuit and said first-named half-section, adjacent half-sections ofeach filter having at their connecting terminals substantially equalconstant-k image impedances, and said filters being relativelyproportioned to present across said output circuit a resultant imageimpedance approximating that of a constantk continuous-band filterpassing the band comprising said contiguous bands.

5. A composite band-pass filter comprising a plurality of input circuitsof different impedances and a common output circuit, a plurality ofindividual band-pass filters passing respectively a series of contiguousfrequency bands and connected to said common output circuit, each ofsaidfilters being terminated at said common end in a half-section oftype B and proportioned according to formulas of type B, each of saidfilters including also one or more impedance matching filterhalf-sections interconnecting its respective input circuit and itsfirst-named half-section, adjacent half-sections of each filter havingat their connecting terminals substantially equal constant-k imageimpedances, and said filter halfsections adjacent said input circuitsbeing of the type A and being proportioned according to formulas of typeA, whereby said filters present across said output circuit a resultantimage impedance approximating that of a constant-k continuous-bandfilter passing the band comprising said contiguous bands.

being terminated at said common" end in an equivalent half-section, eachof said filters nor-" mally including a reactance arm at its termina'end resonant at a frequency of infinite attenuation, each said reactanceam being replaced by reactance'elements of the other filter, each ofsaid filter! including also one or more impedance matching equivalenthalf-sections interconnecting its respective input circuit and itsfirst-named half-section, the equivalent half-sections of .each filterbeing K combined to form composite filter sections for the high and lowbands of the types C and D, respectively, andproportioned according tothe formulas of types C and D, respectively.

7. A composite band-pass filter comprising a pair of individualband-pass filters passing respectively two contiguous frequency bandsand connected at one end to a common terminal circuit, each of saidfilters including a transformer provided with primary and secondarywindings,

a transformer winding of the higher band filter being dividedintosections with the corresponding winding 0! the lower band filterbeing interlosed therebetween, condensers ccnnectedrindivlduaily acrosseach oi. said higher band winding sections and across said lower bandwinding, whereby said higher band filter constitutes terminal reactancearms for said lower band filter, and the lower band filter constitutesthe equivalent of a terminal reactance arm for saidhigher band filter,said transformer windings and associated condensers being proportionedto approximate a constant-k mid-shunt image impedance of acontinuous-band filter over said contiguous bands.

HAROLD A. WHEELER.

